Effect Of Zonal Flow Research Articles

Effects of zonal flows on ion temperature gradient instability in the scrape-off layer of a field-reversed configuration

Gyrokinetic simulations of long wavelength ion temperature gradient (ITG) turbulence in the scrape-off layer (SOL) of a field-reversed configuration (FRC) find that zonal flows are nonlinearly generated and are the dominant mechanism for the nonlinear saturation of the ITG instability. After the ITG saturation, zonal flows remain undamped and gradually suppress the turbulent transport to a very low level. In the simulations with collisions, collisional damping gradually reduces zonal flow amplitude to a lower level, which allows finite ITG turbulence intensity and ion heat transport in the SOL. The steady state turbulence intensity and ion heat transport are found to be proportional to the collision frequency. This favorable scaling suggests that minimizing collisions (e.g. increasing temperature, reducing impurity content, etc) and preserving toroidal symmetry could improve plasma confinement in the FRC.

Reduced models of turbulent transport in helical plasmas including effects of zonal flows and trapped electrons

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

Effects of zonal flows on transport crossphase in dissipative trapped-electron mode turbulence in edge plasmas

Confinement regimes with edge transport barriers occur through the suppression of turbulent (convective) fluxes in the particle and/or thermal channels, i.e. , and , respectively, for drift-wave turbulence. The quantity is the turbulence intensity, while and are the crossphases. For H-mode, standard decorrelation theory predicts that it is the turbulence intensity that is mainly affected via flow-induced shearing of turbulent eddies. However, for other regimes (e.g. I-mode, characterized by high energy confinement but low particle confinement), this decrease of turbulence amplitude cannot explain the decoupling of particle versus thermal flux, since a suppression of turbulence intensity would necessarily affect both fluxes the same way. Here, we explore a possible new stabilizing mechanism: zonal flows may directly affect the transport crossphase. We show the effect of this novel mechanism on the turbulent particle flux, by using a simple fluid model (Baver et al 2002 Phys. Plasmas 9 3318) for dissipative trapped-electron mode (DTEM), including zonal flows. We first derive the evolution equation for the transport crossphase δk between density and potential fluctuations, including contributions from the E × B nonlinearity. By using a parametric interaction analysis including the back-reaction on the pump, we obtain a predator–prey like system of equations for the pump amplitude ϕp, the pump crossphase δp, the zonal amplitude ϕz and the triad phase-mismatch Δδ. The system displays limit-cycle oscillations where the instantaneous DTEM growth rate—proportional to the crossphase—shows quasi-periodic relaxations where it departs from that predicted by linear theory.

Turbulence, transport, and zonal flows in the Madison symmetric torus reversed-field pinch

The robustness and the effect of zonal flows in trapped electron mode (TEM) turbulence and Ion Temperature Gradient (ITG) turbulence in the reversed-field pinch (RFP) are investigated from numerical solutions of the gyrokinetic equations with and without magnetic external perturbations introduced to model tearing modes. For simulations without external magnetic field perturbations, zonal flows produce a much larger reduction of transport for the density-gradient-driven TEM turbulence than they do for the ITG turbulence. Zonal flows are studied in detail to understand the nature of their strong excitation in the RFP and to gain insight into the key differences between the TEM- and ITG-driven regimes. The zonal flow residuals are significantly larger in the RFP than in tokamak geometry due to the low safety factor. Collisionality is seen to play a significant role in the TEM zonal flow regulation through the different responses of the linear growth rate and the size of the Dimits shift to collisionality, while affecting the ITG only minimally. A secondary instability analysis reveals that the TEM turbulence drives zonal flows at a rate that is twice that of the ITG turbulence. In addition to interfering with zonal flows, the magnetic perturbations are found to obviate an energy scaling relation for fast particles.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

Global gyrokinetic simulations of TEM microturbulence

Global gyrokinetic simulations of electrostatic temperature-gradient-driven trapped-electron-mode (TEM) turbulence using the δf particle-in-cell code ORB5 are presented. The electron response is either fully kinetic or hybrid, i.e. considering kinetic trapped and adiabatic passing electrons. A linear benchmark in the TEM regime against the Eulerian-based code GENE is presented. Two different methods for controlling the numerical noise, based, respectively, on a Krook operator and a so-called coarse-graining approach, are discussed and successfully compared. Both linear and non-linear studies are carried out for addressing the issue of finite-ρ*-effects and finite electron collisionality on TEM turbulence. Electron collisions are found to damp TEMs through the detrapping process, while finite-ρ*-effects turn out to be important in the non-linear regime but very small in the linear regime. Finally, the effects of zonal flows on TEM turbulence are briefly considered as well and shown to be unimportant in the temperature-gradient-driven TEM regime. Consistently, basically no difference is found between linear and non-linear critical electron temperature gradients in the TEM regime.

Study of the Effect of the Helical Ripple Transport on the Confinement via Zonal Flows in Helical Plasmas

The role of the effective helical ripple in the helical plasma confinement is analyzed using the transport code via the effect of zonal flows. One-dimensional coupled transport equations are calculated in the different cases of the effective helical ripple. The reduction of the effective helical ripple ratio lowers the criterion for the excitation of zonal flows in helical plasmas. It is demonstrated that the reduction of the turbulent transport can be obtained in the case of the smaller neoclassical transport when zonal flows are excited.

Theoretical Modeling of Transport Barriers in Helical Plasmas

A unified transport model is proposed to study the physical mechanism for the formation of electron internal transport barriers (e-ITB) in helical plasmas and internal diffusion barriers (IDB) observed in the Large Helical Device (LHD). An e-ITB can be predicted with the effect of zonal flows (ZFs) in the low collisional regime when the radial variation in particle turbulent diffusivity is included. The transport analysis in this article shows that particle fueling induces IDB formation when the unified transport model is used in the high collisional regime. After particle fueling, a steep density gradient forms. To examine the density limit for the IDB in helical toroidal plasmas, the effect of radiation loss is included in a set of transport equations.

Bifurcation of Heat Transport in High Temperature Plasma

A second-order phase transition of heat transport, which is characterized by a discontinuity in the time derivative of the temperature gradient, is observed in the high temperature plasma when the radial heat flux is modulated by repetitive pellet injections. The temperature dependence of the heat flux changes at the phase transition between two transport branches: one has a strong temperature dependence as predicted by gyro-Bohm type transport and the other has a weak temperature dependence which is consistent with the transport with the “screened” effect of zonal flow.

Nonlinear saturation of collisionless trapped electron mode turbulence: Zonal flows and zonal density

Gyrokinetic δf particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter-sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear, and electron temperature gradient. For parameters where zonal flow is found to be unimportant, zonal density (purely radial density perturbations) is generated and expected to be the dominant saturation mechanism. A toroidal mode-coupling theory is presented that agrees with simulation in the initial nonlinear saturation phase. The mode-coupling theory predicts the nonlinear generation of the zonal density and the feedback and saturation of the linearly most unstable mode. Inverse energy cascade is also observed in CTEM turbulence simulations and is reported here.

Gyrokinetic δf particle simulation of trapped electron mode driven turbulence

The linear instabilities and nonlinear transport driven by collisionless trapped electron modes (CTEM) are systematically investigated using three-dimensional gyrokinetic δf particle-in-cell simulations. Scalings with local plasma parameters are presented. Simulation results are compared with previous simulations and theoretical predictions. The magnetic shear is found to be linearly stabilizing, but nonlinearly the transport level increases with increasing magnetic shear. This is explained by the changes in radial eddy correlation lengths caused by toroidal coupling. The effect of zonal flows in suppressing the nonlinear CTEM transport is demonstrated to depend on electron temperature gradient and electron to ion temperature ratio. Zonal flow suppression is consistent with the rate of E×B shearing of the ambient turbulence and radial spectra broadening. Strong geodesic acoustic modes (GAM) are generated along with zonal flows.

A new paradigm for plasma transport and zonal flows

Most tokamak experimental results indicate dependence of the ion thermal conductivity on the isotopic mass close to χ⊥∼mi−0.5, i.e., inverse gyro-Bohm. This is in stark contradiction to most present theoretical models predicting Bohm (mi0) or gyro-Bohm (mi0.5) scaling. A basic physics isotopic scaling experiment [V. Sokolov and A. K. Sen, Phys. Rev. Lett. 89, 095001 (2002)] on the anomalous ion thermal conduction due to ion temperature gradient (ITG) instabilities in two different gases (hydrogen and deuterium) closely confirms the tokamak results. Another series of experiments designed to explore the physics basis of this scaling appears to lead to a new model for this scaling based on 3-wave coupling of two ITG radial harmonics and an IA wave. The resulting isotopic scaling of transport is ∼mi−0.5 dictated primarily by the IA damping. This basic physics may be extrapolated to tokamaks resolving the paradox [V. Sokolov and A. K. Sen, Phys. Rev. Lett. 92, 165002 (2004)]. Last, the much discussed theoretical role of zonal flows in transport regulation is critically examined by another set of experiments. A novel diagnostic has been developed on the basis of the observation that the effect of zonal flow can be seen in the FM modulation (at zonal flow frequency) of the carrier frequency of the large equilibrium Doppler shift frequency of ITG modes both in tokamaks and in the Columbia Linear Machine [V. Sokolov, X. Wei, and A. K.Sen, APS DPP meeting, Savannah (2004)]. The present results indicate zonal flow levels close to the theoretical prediction, but its shear is much lower than that predicted by theory for transport regulation.

The effects of zonal flow on nonlinear Rossby waves

In this paper, we using phase plane method have derived the stability criteria of linear and nonlinear Rossby waves under the conditions of semi-geostrophic approximation and have gotten the solutions and geostrophic vorticity of corresponding solitary Rossby waves. It is pointed out that the wave stability is connected with the distri-bution of zonal flow and when the zonal flow is different the solitary wave trough or ridge is formed.

Effects of Zonal Flows on Equatorially Trapped Waves

Linear shallow water equations are employed to study the effects of basic zonal flows on equatorially trapped waves. Analytical solutions are obtained for constant basic zonal flows. It is shown that changes in the wave structures due to the non-Doppler effect of the basic zonal flow are considerable for the Rossby wave, moderate for the westward propagating mixed Rossby–gravity wave, but negligible for the other equatorial waves. The Rossby wave and the westward propagating mixed Rossby–gravity wave possess greater eigenfrequencies and are less trapped in westerlies than in easterlies. The dependence of the Rossby wave structure upon the basic zonal flow is interpreted in terms of potential vorticity conservation. In basic zonal flows with meridional shears, the eigenfrequencies are found to be larger in equatorial easterlies than in equatorial westerlies for the westward propagating waves but smaller for the eastward propagating waves. While the meridional structures of the eastward propagating waves show little sensitivity to the basic zonal flow, the Rossby wave is less trapped in equatorial westerlies but the westward propagating inertia–gravity wave is less trapped in equatorial easterlies. It is suggested, therefore, that the equatorial transient Rossby waves interact with midlatitudes more readily at the longitudes associated with tropical westerlies. Furthermore, at these same longitudes, it is possible that extratropical forcing may project onto the equatorial modes and produce equatorially trapped responses if the forcing lies within their turning latitudes, which may extend to beyond 40° latitude at these locations. The conclusion underlines the upper troposphere of the tropical eastern Pacific Ocean and possibly the tropical Atlantic Ocean as critical regions of latitudinal interaction in both directions over a wide range of time scales.

Effect of Zonal Flows on the Free Oscillations of a Barotropic Atmosphere

Abstract Solutions of the linearized global shallow-water equations (Laplace tidal equations) including the effect of a mean zonal flow are obtained by the Galerkin-transform method. Free oscillations of the first kind (gravity-inertia modes) are little affected by the zonal flow. Solutions of the second kind (rotational modes of the Rossby-Haurwitz type) are significantly affected by a zonal flow different from solid rotation. Only a few lowest rotational modes, whose angular phase velocities are less than the minimum velocity in the zonal flow, appear as discrete. The remaining angular phase velocities fall into a continuous spectrum which covers the interval between the minimum and maximum zonal velocities. An approximate, but accurate, frequency formula is obtained for the discrete modes of free oscillations under the effect of a mean zonal flow. The frequencies and latitudinal structures of a few lowest rotational modes under the effect of a mean zonal flow are examined in detail and compared to obse...